Chargeable Electric Bulb

Google 'emergency lighting' or 'emergency ballast' for fluorescent bulbs. Not exactly what you have described, but close.

Bulbs you plant in the garden, lamps give illumination.

As Bigg said Google emergency lighting. They come in various guises, maintained, non maintained, etc. You will have to decide what suits your application.

There are many but do they incorporate compact Battery and ballast.

Once again see "GOOGLE"

Solar garden lighting fits the description. The power failure can be called "night-time".

Not exactly,I want them to illuminate indoors.

Skylights in the roof?

Solar powered lights don't care if they're indoors or outdoors, they only care about how much light they get to recharge their batteries. Turn off all the "normal" indoor lights at night and be amazed at what you see!

Keep in mind that you can not satisfy the laws of physics (getting something for nothing is a leading cause of this confusion) which states that energy is always conserved.

In other words to do as you described, you will have to (briefly) consume more power than you need, storing what you don't need, for future usage. A battery does that fairly well. Super Capacitors are pretty good at this too, but they have a higher internal resistance than batteries and your best choice for lighting will be LED.

You are talking about maintained mode emergency lighting. Try an internet search for plenty of options, the field is large, even I sell them.

They exist, it's just not terribly popular once people look into it. We have bulbs for light fixtures with built-in battery backup for my 90 year old nearly blind mother, because if the power fails, she could fall. The problem with the concept as it turns out is the switching. In a light fixture, you have a switch that cuts power to the lamp and it stops illuminating. The battery backup feature cannot distinguish this from a power failure. So the battery backed bulb has its own switch above the base, meaning that for a table type light fixture, you now have two switches. This confuses my mother to no end. And of course if you have a ceiling mounted fixture and a wall switch, it becomes a lot more difficult to manage. You must never use the wall switch, it must be left on all the time, so you then need a pull chain switch on the lamp itself.

there will be no bulb with inbuilt battery. but external battery can be connected to a bulb and circuit can be designed to operate it remotely.